[QUE/QFT-06009] QFT-PROBLEM

Let \(n^\mu\) be a spacelike four vector satisfying \(n^\mu n_\mu=-1\), show that

• the eigenvalues of \(\gamma_5n\!\!\!/ \) are \(\pm1\).
• \((\gamma_5 n\!\!\!/)^2 =1\)
• If \(p^\mu n_\mu=0\), \(p\!\!\!/\) commutes with \(\gamma_5 n\!\!\!/ \)
• Free particle solutions \(u(p)\) and \(v(p)\) of Dirac equation \[ (p\!\!\!/ -M )u(p)=0, \qquad (p\!\!\!/  + M)v(p)=0\] can also be taken to be eigenvectors of \(\gamma_5 n\!\!\!/   \)